Elenco dei seminari tenuti al DIMA precedentemente

ore 11:00-12:00 - Raymond H. Chan, Department of Mathematics, The Chinese University of Hong Kong; SIAM Council member

"Flexible methodology for image segmentation"

Abstract:In this talk, we introduce a SaT (Smoothing and Thresholding) method for multiphase segmentation of images corrupted with different degradations: noise, information loss and blur. At the first stage, a convex variant of the Mumford-Shah model is applied to obtain a smooth image. We show that the model has unique solution under different degradations. In the second stage, we apply clustering and thresholding techniques to find the segmentation. The number of phases is only required in the last stage, so users can modify it without the need of repeating the first stage again. The methodology can be applied to various kind of segmentation problems, including color image segmentation, hyper-spectral image classification, and point cloud segmentation. Experiments demonstrate that our SaT method gives excellent results in terms of segmentation quality and CPU time in comparison with other state-of-the-art methods

"Inverse scattering in time domain"

Abstract:In the 90s, many reconstruction algorithms have been developed for imaging in the framework of Inverse Scattering in Frequency Domain; among others, the Point Source Method (PSM) and the Linear Sampling Method (LSM). Many improvements concerning these both algorithms have been achieved in the 2000s. Recently they have been adapted for Inverse Scattering in Time Domain, allowing better reconstructions. We propose to briefly explain the key points of the PSM and the LSM and then to show how the main ideas of these methods are extended in Time Domain.

"Case studies on designing adaptive clinical trials in oncology "

Abstract:The designs presented in this talk are motivated by real-life clinical situations in oncology drug development.
In the first design, a combination treatment (chemotherapy plus experimental compound XYZ) approaches Phase 3 of development with two different regimens/doses of XYZ.
Traditionally, regimen selection would be done by a Phase II study, followed by a separate phase III trial with the selected regimen.
In this talk, an adaptive, seamless phase 2/3 study is suggest instead.
This adaptive design encompasses both treatment selection as well as a confirmatory statistical test of superiority of the combination treatment over the single-agent control (i.e. chemotherapy).
Joint modeling of two time-to-event endpoints is used and flexible Bayesian predictive power tools drive the interim treatment selection.
Simulations show the operating characteristics and are used to compare selection rules and different methods of achieving alpha-level control for the superiority test.
In the second design, a novel, adaptive Bayesian time-to-dose limiting toxicity model is used to guide dose-escalation and determine the safe dose levels of an experimental combination therapy.
A Bayesian model is used to describe time to this toxicity event.
The posterior probabilities of a DLT from this model are used to determine the next tested dose in the the flexible dose-escalation process and assure a a proper quantification of the risks taken throughout the decision-making process.

"Random Sets of Neural Activity"

"Some recent advances on structural meta-analysis"

Abstract:Structural meta-analysis concerns combining information about relationships between variables from independent studies performed under partially comparable circumstances. After a brief introduction to graphical models, some types of combination of Gaussian graphical models, based on different use of the initial information, will be presented. Some algebraic interpretations will also be discussed.

"Towards the geometry of stochastic relaxation in pseudo-boolean function optimization"

Abstract:We analyze the problem of pseudo-Boolean function optimization by introducing the notion of stochastic relaxation, i.e., we find minima of f by minimizing its expected value over a set of probability densities. By doing this, the parameters of the statistical model become the new variables of the optimization problem.
We justify the use of the exponential family in the stochastic relaxation with previous results about the characterization of its topological closure and of the tangent space. We provide a characterization of the stationary points of the relaxed problem, together with a study of the minimizing sequences with reduced support. Finally, we show how stochastic relaxation can be interpreted as a unifying framework for the analysis of classical techniques in linear programming and stochastic optimization.